"HD" versus "SD" color space

This is a technical primer on the differences between commonly-used color
spaces and practical issues surrounding these differences.

This no single HD or SD color space as they are actually many different HD
and SD color spaces. We'll begin by looking at the two most common video standards
in use today- ITU-R BT. Rec. 601 and Rec. 709- as the most common HD and SD
formats derive from them. The two main differences between the Rec. 601 and
Rec. 709 standards are [A] the luma coefficients (and corresponding scale
factors) and [B] the primaries.

Luma coefficients

In both Rec. 601 and Rec. 709, R'G'B' values are converted into Y'CbCr values.
The Y' component in Y'CbCr approximates the brightness information while the
Cb and Cr chroma components approximate the color information. The formula
for forming Y' is as follows:

Rec. 601 Y' = 0.299 R' + 0.587 G' + 0.114 B'

Rec. 709 Y' = 0.2126 R' + 0.7152 G' + 0.0722 B'

Luma coefficients refer to the numbers in front of R', G',
and B'. Notice that they are different for Rec. 601 and 709. This means that
the same input R'G'B' values will lead to different Y'CbCr values
depending on whether Rec. 601 or 709 numbers are used. The choice of luma
coefficients also affects the scale factors used (not shown).

When converting between Rec. 601 and 709 (or sending 601/709-encoded values
down a 709/601 signal path), a color matrix should be applied so that the
resulting R'G'B' values are (practically) the same. Color inaccuracy occurs
when such a conversion is not applied where it should have been applied. When
this happens, achromatic colors like grey and white will stay the same. Saturated
colors however will be shifted in hue and saturation. Certain saturated colors
may also be pushed outside R'G'B' gamut and clipped. Numerically speaking,
the difference is very large. In practice, the difference is subtle and is
usually not noticed. This is partly because:

We aren't very sensitive to (small) color inaccuracies. This is especially
so when there is no side-by-side comparison.

Real world images tend not to contain highly saturated colors (a random
distribution of R'G'B' values would contain much more highly saturated colors).
These errors are strongest for highly saturated colors.

Most film and video material do not contain large patches of color, which
make it easier to discriminate between colors.

These reasons can explain why consumer TV manufacturers can get away with
handling the luma coefficients incorrectly. By omitting the appropriate color
matrix, they can cut corners and reduce cost. But this practice is definitely
wrong and does noticeably impair image quality (most noticeable where highly
saturated colors are being clipped).

In professional post production, this is usually not an issue as most hardware
and software will handle this issue correctly. Nonetheless, this is worth
checking as some software does contain bugs and some cameras can be setup
to encode with different luma coefficients (a dangerous setting in my opinion!).
Sending color bars through the signal path should be done to check that the
signal comes out correctly.

Controversy

At the time Rec. 709 was being formed, there were some who opposed the idea
of changing the luma coefficients. By keeping the luma coefficients the same,
we would have avoided the mess we have now whenever the signal is being decoded
incorrectly. The benefits of changing the luma coefficients on the other hand
are negligible in practice. It reduces the extent of some chroma subsampling
errors for particular color combinations; for other color combinations, it
makes these chroma subsampling errors worse. Many video engineers don't even
think there is a problem with chroma subsampling in the first place and believe
that chroma subsampling is visually lossless (it is not; my article on chroma
subsampling explains and shows why). My opinion is that the change in
luma coefficients has hurt video quality far more than it has improved it.

In any case, we will have to live with the different sets of luma coefficients
between Rec. 601 and 709.

Primaries

Primaries refers to the exact "color" or "shade" of red,
green, and blue. Color is specificied objectively in CIE 1931 x and y co-ordinates.
Obviously there is a need to specify color objectively as there are many different
shades of red, green, and blue.

The 3 sets of primaries in common use today are usually referred to as EBU,
SMPTE C, and Rec. 709. All modern HD formats
use Rec. 709 primaries (there are some obsolete HD formats that do not) while
the standard for SD is either EBU or SMPTE C, depending on the country. There
are also the original NTSC primaries, which are obsolete
and not in current use. Why aren't the NTSC primaries currently being used
today?

When the NTSC standards were developed, the designers envisioned a wide gamut
system where the primaries are much more saturated/pure than what we have
now. The more saturated primaries allow a greater range of highly saturated
colors to be reproduced. It is theoretically ideal to make the primaries as
saturated/pure as possible so that the widest range of colors can be reproduced.

One downside to wide gamut systems is that overall luminance of the display
is lower. Luminance can be increased by making the primaries less saturated.
For this reason, consumer TV manufacturers ignored the NTSC standard in order
to make displays brighter. Early consumer TVs were fairly dim so this might
have been a reasonable compromise.

Later on, SMPTE created the "SMPTE C" standard realizing that there
needed to be a production standard. These primaries were derived from the
Conrac CRT monitors that were commonly used for reference monitoring at the
time. Eventually after that, the EBU created their own standard to reflect
changes in CRT phosphors. The EBU primaries are the standard for PAL countries*.

The Rec. 709 set of primaries are a (silly) political compromise between
the EBU and SMPTE C primaries. EBU red and blue were adopted, with a green
halfway between EBU and SMPTE C.

HD <--> SD Conversions
in practice

Ideally, conversions between HD and SD formats would take into account the
different primaries of the systems being used. If such a conversion were performed,
color bars on a master tape would no longer be correct in the destination
format. For post production facilities, color bars would need to be relaid
onto the new tape so that the tape will pass quality control checks. For post
houses to perform this color space conversion would be a liability. If they
forget to redo the color bars (user error happens), then their tape will not
pass quality control (the first thing they check for is that the color bars
line up) and they can even potentially lose a client for their screwup. And
there is little benefit for them to do these color space conversions correctly-
honestly, nobody will notice. They have little incentive to perform ideal
color space conversions (if they even know about it).

Critical monitoring in practice

The most popular monitors for high-end reference monitoring are the Sony
BVM series CRT monitors**, which use SMPTE C phosphors (they conform to SMPTE
C primaries). These monitors are not ideal for HD monitoring as modern HD
formats (in other words, not the obsolete 1035i formats) call for Rec. 709
primaries. There is sometimes a disconnect between what the standards call
for and what actually happens in practice.

*For some reason, I think that the de facto standard in Japan are the EBU primaries. I have never read the standards for Japan so I don't know the correct answer.
**This article is dated. It was written before December 2008.